The maximum pressure for a specific cartridge is measured in CUP. What does CUP mean and how does that relate to PSI? Why isn't PSI used instead of CUP?

CUP is the abbreviation for Copper Units of Pressure. There is no direct conversion of CUP to PSI by a simple method of multiplication or division. The copper crusher method of determining pressure was the standard method of measuring chamber pressure in the US for many years. The move is on to switch to PSI.
Regards,
HockeyPuck

CUP = Copper Units of Pressure.

CUP doesn't relate to PSI. You can take your favorite load, measure it in a CUP presure barrel and in a PSI pressure barrel and get pressure levels and find a "conversion factor". But if you go to a different caliber OR a different pressure load level and re-do the measurements you will probably find a DIFFERENT "conversion factor".

CUP is measured by drilling a hole in the side of the chamber, fitting it with a small insert that holds a copper cylinder that has been measured to have a specific density to make sure it's solid without any voids etc. Then a shot is fired, the copper cylinder is removed from the insert and measured - the amount it shortened is used with a table to determine the CUP level. PSI measurements are made in a similar manner, but an electronic pressure gauge (based on a pezio-electric (sp?) quartz crystal) is inserted instead of the copper fitting and a voltage is read, then converted to pounds per square inch. Available to the hobbiest are strain gauges that can be fastened to the barrel over the chamber, when a cartridge is fired the steel expands, changing the resistance of the strain gauge. This can be converted to PSI if you have a way of calibrating the strain gauge. Since most of us don't the best we can do is comparitive measurements with factory loads.

Modern cartridges do use PSI load levels, older ones use CUP load levels. It just depends on what kind of pressure barrels were available when the cartridge was formally introduced and spec'ed. Some loading manuals (Hodgdon #27) do have a table of maximum pressures for some cartridges in both CUP and PSI. I think load manuals will start to use only PSI levels as the old loads are re-tested for new editions. No, every load in a loading manual is not re-tested for every edition, usually just new loads using a new powder/bullet etc and new cartridges are tested.

Another one you will see used for very low pressure cartridges and shotgun shells is LUP or Lead Units of Pressure.

The following data are from the 47th Lyman manual, page 93:

..........CUP(000) PSI(000)
22-250....53........62
222 Rem...46........50
6mm Rem...52........65
25-06.....53........63
243.......52........60
257 Robts.45........54
257 +P....50........58
270 Win...52........65
7mm08.....52........57.5
7mm Mag...52........61
7x57......46........51
280 Rem...50........60
30 Carb...40........40
30-06.....50........60
30-30.....38........42
300 Sav...46........47
300 WM....54........64
303 Brit..45........49
308 Win...52........60
8x57......37........35
8 Rem Mag.54........65
338 WMag..54........64
35 Rem....35........33.5
45-70.....28........28

Anyone with a statistical calculator can quickly discover the formula that relates the two. If you want to convert CUP to PSI, enter the CUP data as your X variable and PSI as your Y variable, and do linear regression. I've used slightly different data sets at different times, but you always get a very high R^2 value, about .93, which ends all discussion about whether the two measures are correlated. They are. If someone wants to challenge that, they will have to show that .93 is much closer to 0 than it is to 1. You'll also get a formula something like PSI = -17,902 + 1.51 * CUP, for rifles. I haven't tested pistol data.

Even if the formula were perfect, which it is not, you would still get data points scattered around somewhat off your regression line. This is because both measurement systems are highly imperfect. They cannot tell you exactly how much pressure happened in the chamber, and hence miss the line by a little bit.

The CUP method is only precise enough to place you somewhere within a 5,000 CUP (7,500 PSI) band. A 10 shot average pulls that in to about 1,600 CUP (2,400 PSI).

The European CIP publishes max pressure numbers in both CUP and PSI (they measure pressure at the mouth of the cartridge, rather than the middle of the cartridge, as SAAMI does), and, from an examination of their data, it is clear that they have abandoned doing both measurements. They are only doing one of the two, and using a formula like the one shown to create the other. So if you "know" that there is no conversion, please don't tell the Europeans. Their equivalent of SAAMI has apparently been doing it successfully for years.

For European measurements, the conversion is PSI = -2809 + 1.21 * CUP, and the R^2 is .997

See April 2003 Varmint Hunter for a more complete discussion.

[ 11-16-2003, 20:18: Message edited by: denton ]

Loading references before the early 1970s will ordinarily say PSI, but they were usually measured by the copper (or lead) crusher method. When the piezoelectric systems became more widely available to loaders (I have a book on "Electron Tubes in Industry" from 1937, BTW, that shows such devices complete with schematics) they had to make a distinction because the results varied widely depending on the method of measurement. Thus we got CUP (and LUP.)

I have always thought it would be very worthwhile to have pressure barrels fitted with both systems. That was until I telephoned Hodgdon and asked them why they didn't do that. It is very expensive.

Since it's compressing a piece of copper, I think that both the time near peak pressure and the total area under the pressure-time curve could affect the results of the crusher method.

you could do a least squared regression and determine a y=mx+b for it but it would NOT have any relation to reality, imho.

jeffe

I have heard it claimed that CUP is closer to reality (force on the gun)
than PSI as it is measuring the deformation of metal.
One observation; Straight cases 30 carbine, ans 45/70 measure the
same in CUP, and PSI. Could there be somthing like a reflection going on
with necked cases?.
Good luck!

I'm not sure we can generalize that that's true of straight cases from seeing .30 Carbine and .45-70 data.

If you will take the time to make an XY graph of the values given, the linear relationship will quickly be apparent. Put CUP on the horizontal axis, and PSI on the vetical axis, and plot all the points. Once you do that, you'll see how it works. If the two variables were uncorrelated, you'd get a "shotgun splat". You don't get that. You get a cluster of data that is fairly tight around the line. That's the definition of correlated.

The reason that all the points do not fall exactly on the line is that neither the piezoelectric nor the CUP system is very precise. Whatever pressure is attained in the chamber is only approximately registered on the measuring device. Since you will never know how much pressure actually happened, you will never get a perfect fit to the line.

For the math minded, the PSI registered on a piezoelectric transducer is some function (mathmatical expression written in terms of) of chamber pressure. The CUP reading found by crushing a copper pellet is a different function of chamber pressure. PSI and CUP are different functions of the same variable. There has to be a formula to convert from one to the other. If there were no formula, then at least one of the measurement systems would have to be worthless, and we know that is not true.

The argument that the amount the copper pellet is crushed is a function of the area under the pressure curve is often stated, and is correct. However, it is an distinction without a difference. It turns out that practically all the deformation happens at peak pressure, and that you can take the deformation of the copper pellet as a good indicator of peak pressure, which is what its designers wanted it to indicate.

So try the graph thing. It clarifies things a lot. Remember, you'll never know how much pressure happened in the chamber, because both measurement systems are very imperfect. For any given round, neither system can reliably distinguish 58,000 PSI from 62,000 PSI. That difference may be important to you, but the measurement systems we're stuck with simply cannot tell them apart for a single round.

The other thing to bear in mind is that CIP in Europe is using exactly this technique to generate two sets of published numbers, PSI and CUP, based on a single test.

[ 11-17-2003, 02:53: Message edited by: denton ]

Just take a look in the A^2 manual. The extreme spread on PSI for the same load, bullet, rifle ranges from 5k to sometimes 9k psi. This might not be up to laboratory standards, but at least shows the degree of correlation that Denton calculates is well within experimental tolerance, and to a first order, can get you in the ball park.

regards,

steve

It seems to me that the cup method averages over more time than the psi.

Of course niether averages over the correct time interval with just the corrections for predicting when the brass will be over stressed.

For that, you would have to look at the brass.

I don't think it's quite as bleak as eldeguello does, though I understand his angst.

The first thing is that anything you read in a reloading manual is an estimate. If you treat it that way, you'll be cautious, and work your loads up from a reduced load.

The second thing is that the formula is a handy way to fill in values you don't have. I reload the 7.62x54R, and it took a bit of research to come up with a CUP limit for it. Then I needed to convert to PSI, which I can measure. That's about the only way to get an "adult" load for it.

The third thing is that a careful home experimenter can produce PSI measurements that are as repeatable as the best piezoelectric PSI measurements that are published, and that are better than most.

Almost all the numbers we deal with on a day to day basis are estimates. It's not bad to have estimates, but it does help to understand their accuracy and precision. That way, you don't make bad decisions, by assuming that the numbers given are "right on the nose".